Model 3

Description of the model


This third model is again a slight variant of the two first, in which we assign a specific \(\alpha\) to each predator, but we also divide it by the degree of the predator (number of preys). In doing so, we can still isolate difference between predator, to check if some predator seems to be different from the whole, but also try to divide between each of ones predators prey. \[\begin{align} F_{ij}^{real} &= \frac{\alpha_{j}}{D_{j}} * B_i * \frac{B_j}{M_j} \end{align}\]

This model was fit with a hierarchy implemented on the alpha parameter. A global alpha was estimated, with 118 respective unique alphas for each predators. In contrast with model 2, the alphas in model 3 are divided by the predator’s degree.

Summary table

Summary table model 3
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
a_pop -10.020670 0.0153252 0.3601779 -10.735072 -10.268143 -10.016719 -9.775512 -9.322804 552.3597 1.0070492
a_sd 3.847411 0.0019136 0.2664588 3.362061 3.664654 3.833639 4.016568 4.406197 19388.7332 0.9999259
sigma 1.679814 0.0003024 0.0410108 1.601866 1.651454 1.678931 1.706225 1.763753 18389.1117 0.9999737

Exploring parameters posterior distribution

General parameters

Respective predator alphas

Rhats

Examining Rhats to see if all parameters have converge

Simulated data vs observed data